Gradient-based methods are a prototypical family of "explainability for AI" (XAI) techniques, especially for image-based models. However, they (1) require white-box access to models, (2) are vulnerable to adversarial attacks, and (3) produce attributions that lie off the image manifold, leading to explanations that are not amenable to human perception. To overcome these challenges, we introduce Derivative-Free Diffusion Manifold-Contrained Gradients (FreeMCG): by leveraging ensemble Kalman filters and diffusion models, we derive a derivative-free approximation of the model’s gradient projected onto the data manifold, requiring access only to the model’s outputs (i.e., black-box setting). We demonstrate the effectiveness of FreeMCG by applying it to both counterfactual generation and feature attribution, which have traditionally been treated as different tasks requiring distinct methods. Through comprehensive evaluation on both counter-factual explanation and feature attribution we show that our method yields state-of-the-art results for both tasks while preserving the essential properties expected of XAI tools. Code: https://github.com/one-june/FreeMCG.

Diffusion models have shown impressive results in generating high-quality conditional samples using guidance techniques such as Classifier-Free Guidance (CFG). However, existing methods often require additional training or neural function evaluations (NFEs), making them incompatible with guidance-distilled models. Also, they rely on heuristic approaches that need identifying target layers. In this work, we propose a novel and efficient method, termed PLADIS, which boosts pre-trained models (U-Net/Transformer) by leveraging sparse attention. Specifically, we extrapolate query-key correlations using softmax and its sparse counterpart in the cross-attention layer during inference, without requiring extra training or NFEs. By leveraging the noise robustness of sparse attention, our PLADIS unleashes the latent potential of text-to-image diffusion models, enabling them to excel in areas where they once struggled with newfound effectiveness. It integrates seamlessly with guidance techniques, including guidance-distilled models. Extensive experiments show notable improvements in text alignment and human preference, offering a highly efficient and universally applicable solution. See Our project page : https://cubeyoung.github.io/pladis-proejct/

Diffusion models have recently attained significant interest within the community owing to their strong performance as generative models. Furthermore, its application to inverse problems have demonstrated state-of-the-art performance. Unfortunately, diffusion models have a critical downside - they are inherently slow to sample from, needing few thousand steps of iteration to generate images from pure Gaussian noise. In this work, we show that starting from Gaussian noise is unnecessary. Instead, starting from a single forward diffusion with better initialization significantly reduces the number of sampling steps in the reverse conditional diffusion. This phenomenon is formally explained by the contraction theory of the stochastic difference equations like our conditional diffusion strategy - the alternating applications of reverse diffusion followed by a non-expansive data consistency step. The new sampling strategy, dubbed Come-Closer-Diffuse-Faster (CCDF), also reveals a new insight on how the existing feed-forward neural network approaches for inverse problems can be synergistically combined with the diffusion models. Experimental results with super-resolution, image inpainting, and compressed sensing MRI demonstrate that our method can achieve state-of-the-art reconstruction performance at significantly reduced sampling steps.

Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step followed by a projection-based measurement consistency step, often produce sub-optimal results. By studying the generative sampling path, here we show that current solvers throw the sample path off the data manifold, and hence the error accumulates. To address this, we propose an additional correction term inspired by the manifold constraint, which can be used synergistically with the previous solvers to make the iterations close to the manifold. The proposed manifold constraint is straightforward to implement within a few lines of code, yet boosts the performance by a surprisingly large margin. With extensive experiments, we show that our method is superior to the previous methods both theoretically and empirically, producing promising results in many applications such as image inpainting, colorization, and sparse-view computed tomography. Code available https://github.com/HJ-harry/MCG_diffusion

Optimal transport (OT) is a mathematical theory that can provide a tool how to transfer one measure to another measure at minimal cost, thus serve another framework for computer vision tasks of image processing without reference. Cycleconsistent generative adversarial network (cycleGAN) is a recent extension of GAN to learn target distributions with less mode collapsing behavior, and also does not need matched data during training. In this article, we explain the link between these two framework by mathematical formula and experimental results. We prove that cycleGAN architecture can be derived from optimal transport problem, and this implies that cycleGAN is a plausible way to learn target distribution when it comes to handling data far from the training set. Using accelerated MR imaging experiments, we confirmed the flexibility and efficacy of our theoretical framework.

To improve the performance of classical generative adversarial networks (GANs), Wasserstein generative adversarial networks (WGANs) were developed as a Kantorovich dual formulation of the optimal transport (OT) problem using Wasserstein-1 distance. However, it was not clear how CycleGAN-type generative models can be derived from the OT theory. Here we show that a novel CycleGAN architecture can be derived as a Kantorovich dual OT formulation if a penalized least squares (PLS) cost with deep learning--based inverse path penalty is used as a transportation cost. One of the most important advantages of this formulation is that depending on the knowledge of the forward problem, distinct variations of CycleGAN architecture can be derived: for example, one with two pairs of generators and discriminators, and the other with only a single pair of generator and discriminator. Even for the two generator cases, we show that the structural knowledge of the forward operator can lead to a simpler generator architecture which significantly simplifies the neural network training. The new CycleGAN formulation, which we call the OT-CycleGAN, has been applied for various biomedical imaging problems, such as accelerated magnetic resonance imaging (MRI), super-resolution microscopy, and low-dose X-ray computed tomography (CT). Experimental results confirm the efficacy and flexibility of the theory.